Never heard about such thing. You could do this with checking the error message and then prompting for password. However this is a modification of Nautilus, not a simple addon, since I don't think Nautilus supports such addons. (Guess you could write this on a code freelancer page. You pay x$ if someone writes a nautilus fork with this feature. Well.. not a long term solution.)
Basically you could write a .sh script for the backup and run that with sudo, OR simply use sudo cp -R
... something like that. (Rsync?)